A variant of the classic SAV approach, called the exponential-SAV (ESAV) scheme, was studied in [1]}.
We below summarize the ESAV method, also with a stabilization term based on the energy splitting (REF ).
Define the auxiliary variable by \(r(t)=\exp \lbrace E_2(u(t))\rbrace \) 
and reformulate (REF ) as
\(& u_t = \varepsilon ^2\Delta u - \kappa u + \frac{r}{\exp \lbrace E_2(u)\rbrace } (f(u)+\kappa u), \\& (\ln r)_t = - \frac{r}{\exp \lbrace E_2(u)\rbrace } (f(u)+\kappa u,u_t).\) 
